Another one: An ellipse is traced out as the loci of the sum of the distance between the point and two foci.

To make sure my definition is clear (I didn't bother to look it up to find a good one) to find the equation for an ellipse with two given foci F1 and F2, propose a point (x, y) and set up the distance relations such that the sum of the distances between F1 and (x, y) and between F2 and (x, y) is some constant.